Could be a wiring issue aswell. If the connection between the module and the sensor is broken, the module will of course never see a "hit" on the dryer sensor if the sensor is shorted by damp laundry, but the signal is broken by a missing connection.
You'd need a multimeter to check that.
Disconnect the wires from the sensor to the module on the module side and check with one tip connected to one sensor bar and one to one lead for continuity (so a low "Ohm" setting or just continuity test).
Do that to both sides - one lead should be connected to one bar, the other to the other with a very low resistance.
The leads to each other should be open line.
If that is true the fault basically has to be with the board.
Since the exhaust temp is kept correctly and the cooldown is ended correctly apparently (the 3min should include the minimum cooldown period of 2min) the NTC is probably fine.
So the fault you are describing is the moisture sensor thinking there is no load most likely - which means the signal is broken somewhere, either in the wiring or on the board.
If the wiring checks OK take a look at the board.
Since a lot of components appear to be through-hole on this board, soldering them off or on is easy enough for anyone who knows how to solder.
A burnt or broken component should be easy to spot - look at the front of the board with all the parts.
Look for obviously broken connection leads or otherwise physically broken components or even missing components (just 2 leads with nothing on them).
Resistors (the slim long usually orangy things with bands on them and leads on either side) usually look overheated/burned when broken.
Capacitors (can like things with the 2 leads usually on one side next to each other) often fail by "blowing out" with domed or burst top/bottom side.
Since you just transported the dryer, broken solder joints could be very likely aswell.
They *might* be easy to spot if really broken - if look at all the side of the board with all the connections (backside) if any of these small metalic connection spots looks cracked and/or the component connected to it is physically "loose" in there, these will need to be redone.
If anything minor like that jumps out to you in that regard, since you probably don't know how to solder, it might be worth a try to post an add to a market place site like Facebook Marketplace or such and offer a 10er or so to redo that solder joint or change out that component.
If these boards fail, it usually only is one small fault, one single component, and for somebody desoldering and resoldering a single component is an easy 10$ to make yet still cheaper to you.
If you can't easily see/check any of these things and/or replacement boards are cheap and easy/quick to get, going for a new board might be easier of course.